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%I #21 Jan 26 2021 10:50:54
%S 1,26,281,2827,28288,282895,2828967,28289681,282896824,2828968252,
%T 28289682538,282896825395,2828968253967,28289682539681,
%U 282896825396824,2828968253968252,28289682539682538,282896825396825395,2828968253968253967,28289682539682539681
%N a(n) = Sum_{k=1..9} floor(10^n / k).
%H Reinhard Zumkeller, <a href="/A130901/b130901.txt">Table of n, a(n) for n = 0..100</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (11,-10,-1,11,-10).
%F A055642(a(n)) = n.
%F From _Chai Wah Wu_, Jan 14 2021: (Start)
%F a(n) = 11*a(n-1) - 10*a(n-2) - a(n-3) + 11*a(n-4) - 10*a(n-5) for n > 7.
%F G.f.: (-5*x^7 - 2*x^6 + 2*x^5 + 16*x^4 - 3*x^3 + 5*x^2 + 15*x + 1)/((x - 1)*(x + 1)*(10*x - 1)*(x^2 - x + 1)). (End)
%e a(1) = [10/1]+[10/2]+[10/3]+[10/4]+[10/5]+[10/6]+[10/7]+[10/8]+[10/9] = 10 + 5 + 3 + 2 + 2 + 1 + 1 + 1 + 1 = 26;
%e a(2) = [100/1]+[100/2]+[100/3]+[100/4]+[100/5]+[100/6]+[100/7]+[100/8]+[100/9] = 100 + 50 + 33 + 25 + 20 + 16 + 14 + 12 + 11 = 281.
%o (Python)
%o def a(n): return sum(10**n//k for k in range(1, 10))
%o print([a(n) for n in range(20)]) # _Michael S. Branicky_, Jan 26 2021
%o (PARI) a(n) = sum(k=1, 9, 10^n\k); \\ _Michel Marcus_, Jan 26 2021
%Y Cf. A055642, A130890.
%K nonn,easy
%O 0,2
%A _Reinhard Zumkeller_, Jun 08 2007
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